They didn’t invent “elasticsearch” from scratch, rather they took someone else’s codebase (Lucene) and made it better. Fundamentally that’s what AWS did too... they took open source code and improved on it to offer a very popular managed service. Elastic seems annoyed that AWS has executed better on the managed service front but aren’t offering up strong reasons for this being “NOT OK”. Elastic was happy to use code and concepts from others to build their product but seem annoyed when others did the same to them. I don’t get it.
The brand name thing might have more weight but it will come down to if they were truly enforcing the name the whole time they owned it or are just annoyed with AWS. If the name fell into common use they they likely won’t have much luck protecting it.